# Solving Systems of Differential Equations

Is it possible for SageMath to find a general solution for p in terms of x (or p in terms of t) given this system of differential equations?

https://quicklatex.com/cache3/02/ql_8...

https://quicklatex.com/cache3/35/ql_d...

https://quicklatex.com/cache3/02/ql_b...

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WARNING : Corrected a typo from a previous version ...

FWIW, the ODE system is :

[diff(p(x), x, x) == 5*p(x)/(5*p(x)^2 + 4*t(x)^2),
diff(t(x), x, x) == -4*t(x)/(5*p(x)^2 + 4*t(x)^2),
diff(t(x), x) == 1/(5*p(x)^2 + 4*t(x)^2) + diff(p(x), x)]


$$\left[\frac{\partial^{2}}{(\partial x)^{2}}p\left(x\right) = \frac{5 \, p\left(x\right)}{5 \, p\left(x\right)^{2} + 4 \, t\left(x\right)^{2}}, \frac{\partial^{2}}{(\partial x)^{2}}t\left(x\right) = -\frac{4 \, t\left(x\right)}{5 \, p\left(x\right)^{2} + 4 \, t\left(x\right)^{2}}, \frac{\partial}{\partial x}t\left(x\right) = \frac{1}{5 \, p\left(x\right)^{2} + 4 \, t\left(x\right)^{2}} + \frac{\partial}{\partial x}p\left(x\right)\right]$$

( 2023-02-09 10:17:32 +0200 )edit

Is there anything more than that I would have to enter to specify that I want it to be solved?

( 2023-02-09 20:22:57 +0200 )edit